Back at Work

Now back from a week away, mostly spent in Cambridge. Among the accumulated items of interest:

Inference has a review of my book, Woit’s Way, by Andrew Jordan. I like the way it starts out:

Quantum Theory, Groups and Representations is based on a series of lectures that he gave at Columbia University.

And it is excellent.

The review gives a very good explanation of what’s in the book, what level it’s at, and what I’m trying to accomplish. Besides getting all this right, he also gets right some of the things that could have been done better (I did the indexing and I’m kind of lazy, it should have at least twice as many entries).

By the way, when I was in Cambridge I spent a couple days at the conference in honor of Bert Kostant, who was a major figure in the study of the relation of representation theory and quantization. Among the talks there, David Vogan gave a survey talk on Quantization, the orbit method, and unitary representations. He explains clearly the fundamental relationship between representation theory and quantum theory that is central to my book. Roughly the first half of the talk corresponds to topics discussed in the book. I decided to not write about the topic of the second half of Vogan’s lecture, the representation theory of reductive groups and the orbit method, since that would take the book in a different direction, one currently of more interest to mathematicians than physicists (and Vogan has already done a better job of writing about this topic than I ever could).

Also in the new issue of Inference are several pieces commissioned as responses to Natalie Paquette’s wonderful survey article A View from the Bridge about topological QFT and influences running from physics to mathematics. These pieces include takes on the relation of math and physics from Édouard Brezin, John Iliopoulos, Hirosi Ooguri and Martin Krieger, as well as a rather odd one from string theorist Xi Yin.

the deepest and most far-reaching ideas of physics are not the most elegant or beautiful, but the ideas that are confusing, not rigorous, improperly formulated, or, in fact, utterly incomprehensible to mathematicians.

One problem is that many of the examples he gives of “ugly” physical ideas (for instance, spontaneous symmetry breaking) are ones that I think most mathematicians would describe as rather beautiful. He’s right that some of the examples he gives (e.g. complex string theory calculations) are ones that mathematicians wouldn’t find that beautiful, but often these are calculations that have been unsuccessful in their goal of making contact with reality. Yin ends with:

I believe that part of the job of a theoretical physicist is to make the lives of mathematicians miserable. There are, incidentally, few things I can think of that could make a mathematician more miserable than reading Leonard Susskind’s papers.

This includes a footnote to this recent paper by Susskind, and he’s right that this is not one mathematicians would think highly of. For good reason though, with Yin’s implication that this is an important idea in theoretical physics something I find rather dubious (but then again, some would say I’m a mathematician…).

Truly bizarre is Yin’s response to the fact that string theory has failed to make any connection to observable physical reality:

I couldn’t help but notice a striking parallel with the way mathematics became detached from physics during the nineteenth century and, in particular, the outrage that accompanied Cantor’s transfinite set theory and Hilbert’s non-constructive proofs. Was the kind of mathematics that could never be exhibited with real objects actual mathematics, or was it theology? With the benefit of hindsight, we now know that the mathematics flourished like never before during the twentieth century. One can only hope the same thing happens with string theory in the decades to come.

So, having no connection to experiment and observation is not a bug, but a feature, exhibiting a radical new advance in how to do physics? This takes the “post-empirical” thing even further than I’ve seen anywhere else.

Michael Harris at his book’s blog tells the story of how he was commissioned by New Scientist to write something about Peter Scholze’s ideas. His draft ended up not getting used, luckily for us he includes it in the blog posting. New Scientist did however end up publishing a story about this, under the headline The Theorem of Everything (non-paywalled version here).

The Simons Foundation has just put out its 2017 annual report. To get some idea of their increasingly large influence on mathematics and physics research, here are some numbers:

Mathematics and physical sciences receive 31.77% of the grant money. To get a sense of the scale of this, one could compare the fraction of expenses corresponding to math and physical sciences (31.77% x \$409 million= $130 million) to the FY 2017 NSF budget numbers

If you’re going to apply “31.77%” to the entire budget of the Simons Foundation (including things like “depreciation and amortization” and “taxes”), then it makes more sense to compare it with the total “Mathematical and Physical Sciences” part of the FY2017 NSF budget, which is \$1.349 billion. That figure doesn’t include whatever part of the \$200 million “Major Research Equipment & Facilities Construction” goes to mathematical and physical sciences (e.g., about \$90 million for telescope construction), so it’s an underestimate.

Funding at a level roughly 10% of that which NSF provides is pretty damn impressive, but not quite “getting up to the NSF level” yet. (And this of course doesn’t include the funding that NASA and DoE provide.)

While we’re on the topic of the Copenhagen interpretation, you might be interested in Tim Maudlin’s combined review of Adam Becker’s book, “What Is Real?” (mentioned in Philip Ball’s blog), with Errol Morris’ “The Ashtray: (Or the Man Who Denied Reality)”, a very critical look at Kuhn and his ideas: